2010 Prius - Brake whooshing sound after part 4705047140 (master cylinder) replacement

The part you replaced is the one on top or the one on the bottom? How did you bleed the system? This generation goes through a bleeding method where the stroke simulator (I think that's the name) has to be bled after the replacement.

 

OP's part number looks to be the higher up component on the firewall, not the down lower one with "pump" in the name, and looks like a pair of beer cans.

FWIW, dealerships tend to replace both components, rather than gamble. The lower one is signifcantly "cheaper", around $600 USD IIRC.

 

The whooshing sound just means there's air. The ECU picks a target brake pressure, and applies fluid from the accumulator until that pressure is reached. When there's no air, the brake fluid (which isn't compressible) hits the target pressure very quickly, no whoosh. With bubbles, the valve has to stay open long enough to whoosh enough fluid into the passage to compress the bubbles up to the target pressure: whoosh.

You might also notice a matching whoosh, or a bark/quack/honk sound, when you're releasing the brakes and the bubbles expand again, whooshing the fluid back to the reservoir, but what exact sounds you get or don't get can vary.

Just repeat the complete after-actuator-replacement bleed procedure, selected with a scan tool.